Went Bali last December for 6D5N. Generally I feel quite safe walking around with DSLR. The local are very friendly, no interest in robbing you... There are few instances I left my DSLR inside the car, nothing happen, in other countries gone case with shattered window already. Be careful of the monkeys near the temple and monkey forest though, they will grab your things if you don't hold it tight.
Try to dig out the old thread in this section regarding Bali, fellow CSers went and recommended few places to shoot. Rice terrace, temples, sun set, the volcano, few lakes, their culture and architecture. I hired a driver for the trip, he quite good, PM me if you want the driver's contact. Don't recommend driving yourself, the road is very narrow and a lot of motorcycles coming from no where.
Bali felt quite safe to me. In the touristy places, lots of people carrying DSLRs and I didn't hear of any muggings. But then again there's no such thing as "definitely safe", so it always pays to be cautious.